I have known for ages when twist is desirable and how to trim by leech teltales but have always struggled to understand it from a physics point of view which I always like to do.
In particular I struggled with the idea that a narrower angle to the wind was desirable at the top of the sail due to higher a wind speed up there. I totally get that there is more wind up there but it always seemed to me that the opposite solution should be the case as for example when one experiences higher apparent wind let's say in a fast beach cat then one can't sail as close to the true wind and bearing away is necessary as opposed to decreasing the angle.

I found this video interesting particularly at 5:22. The bit about the earth's rotation and different twist being required on port tack from starboard tack due to this phenomenon and the analogy to a water vortex going down a drain was particularly interesting.

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I believe it is along the same lines of a boat sails at it's fastest On a reach .

The vid seems pretty good. There's very few boats that want the head of the main to be at a tighter angle than the foot of the main. Some masthead boats like it in some conditions but I think that's largely because at the head, the jib is so close that it affects the flow over the whole chord main enormously in that area.

Mark Drela, MIT professor and a great aerodynamicist who has designed America's Cup wings, notes that the actual angle of any specific area of the sail to the wind is irrelevant. What is important is the overall flow. He noted that a very tight leach (or having the boom a long way to windward as was done in Etchells and TP52s etc at times) won't necessarily slow a boat because even if the force in that particular area may seem to be having a vector that would slow the boat, it's the effect of the whole airflow that counts.

Some classes that do have the upper leach at a tighter angle than the foot are often ones like Lasers and Windsurfer LTs, where the rig geometry means that there's no way to reduce the leach tension and therefore you have to put up with a leach that is too tight for light winds.

One other point is that the most aerodynamically effective shape is an elliptical span loading. However, "span loading" is a product of depth, chord and angle of attack. If you have a "pinhead" main then it has a very small chord at the top, so to give it more loading (ie make it give more lift) you must increase the angle of attack if possible. That means that although the head is small in area, it's generating a lot of lift for its area and therefore has a higher span loading for its chord.

Conversely, you want the bottom of the sail, where it has a lot of area, to have lower lift (ie loading) for its size than the middle and top, or else you don't get an elliptical span loading but a triangular one. So you actually often have a flatter shape at the bottom.

So a boat with a "pinhead" main uses a very tight leach to reduce the aero drag. A squaretop has lots of area up top so it doesn't need to "load up" that area and therefore can have a more twisted and flatter shape. Plus there's the other issue which is that if you don't twist a pinhead enough then even if it stalls there's not too much area so you won't slow down too much. On the other hand if you have a squaretop that's not twisted enough and therefor stalls, there's a LOT of area stuffing you up and you really hit the brakes.

I've been lucky enough to sail with a couple of the trimmers from Australia II etc and interview a bunch of top sailmakers for my old job, and never heard any of them mention coriolis effect as a practical factor in twist. Given the many other factors involved in changing shape from tack to tack it would seem to be almost impossible to assess.

For sure a complex problem - wind shear and gradient.

See good article here with many useful links.

sailzing.com/wind-shear-and-gradient/

Good links here which you would have seen from NorthU on mainsail trim - believe there is a companion genoa trim one but can't find it at the moment.



northu.com/sailtrimsimulator/

As alluded to by Chris masthead and fractional rigs have different sail twist scenarios for jib and main.

Pretty dumb stuff - Coriolis - gimme me a break - how are you going to determine that? Also the Coriolis is really really weak and so hard to observe that it can only happen on massive scale. Look up Veritassium and Smarter every day to see the puny forces involved. You have the physics backwards. Because the wind velocity is higher up high, then the boat is going relatively slowly compared to the wind, so you need some twist to have the top of the sail eased off. Down low, the boat is going relatively faster through the airflow, so you have to sheet on more (like on a fast cat or skiff)
And "more twist for depowering" , where does the guy make this stuff up? In dinghies or boats with powerful rigs you pull the vang on as the wind gets up, no one fast ever eases the vang off as the wind blows up. Maybe old masthead rigged boats could, but be really careful of doing this on a fractional boat - that is why we play travellers - to keep twist low and ease the main out. There are so many exceptions to twisting off for depowering it is useless advice. I reckon that with everything else you have to do in a race you put a leech telltale in at 1/4 to 1/3 of the way down the leech. Then you ensure that is intermittently flowing, put a couple more in to help if needed. Going upwind or on a reach - ease sheet to get leech telltale working, then sheet on and reduce twist till it stops and hides to leeward, then ease again. With puffs and lulls that will keep you busy all race. Maximum twist in light and choppy conditions, not when depowering.
cheers

Phil

My understanding, and what I do in practice, is to twist off the top of the main. The wind speed at the top of the mast is higher and changes the apparent wind angle and therefore the angle of attack. That Sail simulator is good fun. Here's a screen shot. I've added two red lines indicating sail foot and top angles.

Like Kankana says.
Wind shear is different and depends on height of boundary layer but most rigs not higher enough or moving fast enough to be a major issue.